But Fleming said he wants to continue playing in the side and stay in charge of the Test team.
The 34-year-old opening batsman had been in charge for 10 years, leading his country in 218 one-day internationals, including three World Cups and two semi-finals, New Zealand losing by nine wickets to Pakistan in 1999.
"I want to keep playing but I'm standing down as captain of the one-day side," Fleming, who won 98 and lost 106 one-dayers as skipper, told reporters.
"I still want to captain the Test side," added Fleming, who became skipper in the longer format at the same time as taking over the reins in the one-day team. "I've only just turned 34 and I think I've still got some good batting years ahead of me."
He added: "I want to concentrate on that for a while but I want to put a lot of energy into our Test cricket.
"I'd like to keep playing one-day cricket but as a batsman. In some way your energy levels are sapped when you captain the side.
"I want to play that with a fresh mind and finish off my career with some stats that I think I'm worth," said Fleming, who averages just under 33 in 280 one-day internationals with only eight hundreds.
"Obviously, I'd dreamed the dream of lifting the Cup and saying 'thanks very much' but it's not to be," said Fleming after New Zealand, yet to reach the World Cup final, had lost their fifth semi-final in the tournament's nine-edition history.
"It's been mapped out for some time. But from a professional point of view, it's important we get some fresh ideas.
"I'm very proud of what we've achieved. 218 games as captain is a long time and, professionally, I think I've done the job well. Whoever takes over, I want to be around to assist. I've no problems stepping back."
Asked, who his successor should be, Fleming mentioned experienced left-arm spinner Daniel Vettori, still only 28, as a possible candidate.
"The way we've groomed Daniel Vettori for this tournament, he will certainly come into discussion."
However, with coach John Bracewell's contract now up for review, Fleming added: "But there's going to be a lot of change within New Zealand cricket.
"I'm not sure what John's doing, the selectors are doing, so it's probably a bit presumptuous to recommend Daniel but he's done a fine job up to this point."
And he said that having separate captains for the Test and one-day teams would not be a source of tension. "I've thought long and hard about that. I'm positive it's the right way.
"It gives a guy who takes over the one-day reins a chance to work on that before taking the Test reins rather than putting him into the deep end."
Fleming, widely regarded as one of the best tacticians currently in world cricket, said he's enjoyed the "subtleties" of captaincy.
"Being able to fend the media off for 10 years is a feather in the cap," he joked. "But when you work players out, that's what I get the most joy from."
Sri Lanka captain Mahela Jayawardene, whose unbeaten 115 was the centrepiece of his side's conclusiv victory, said "Stephen's been a great leader for quite some time now.
"Even when I started he was captaining. You could learn a lot from him. With the resources he's had, he's built up a very decent team.
"He's been one of the top captains for the last 10 years."